This study involved an investigation of the relationship between the kinds of solution representations Chinese and U.S. students
use and the sorts of pedagogical representations Chinese and U.S. teachers use during instruction. The findings suggest that
the representations teachers use influence the representations their students use and, hence, have an impact upon the students’
problem solving. One of the practical implications of the findings is that if students are given the opportunity to construct their
own representations of mathematical concepts, rules, and relationships, they also should be encouraged to develop the ability to
use symbolic representations, rather than to rely on concrete ones. In addition, the finding that the Chinese teachers in this study
overwhelmingly used symbolic representations for the solutions of instructional tasks, whereas the U.S. teachers relied almost
exclusively on verbal explanations and pictorial representations, indicates that pedagogical practice is constrained by social and
cultural factors.
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